Multi-layered structure characterization

ABSTRACT

A method and an apparatus ( 10 ) for characterising a multi-layered structure ( 28 ) during formation of said multi-layered structure are disclosed. The method includes the steps of measuring the complex reflectivity of the multi-layered structure ( 28 ) at a wavelength outside of the bandgap of the multi-layered structure ( 28 ) and calculating a complex coupling coefficient from the measured complex reflectivity of the multi-layered structure ( 28 ) continuously or at intervals during the formation process. The apparatus ( 10 ) includes an interferometer ( 24 ) for creating writing beams ( 20, 22 ) to form the multi-layered structure ( 28 ), such as a Bragg grating, in an optical fibre ( 16 ) and an interrogation unit ( 40 ) for measuring the complex reflectivity and for calculating the complex coupling coefficient of the multi-layered structure ( 28 ) and for producing a feedback sigal which is communicated back to the interfemometer ( 24 ). The interrogation unit ( 40 ) includes an optical circuit with Mach-Zehnder or Sganac/Michelson interferometer arrangement.

CROSS REFERENCE TO OTHER APPLICATIONS

This Application is a National Phase of International Application No.PCT/AU03/00296, filed on Mar. 12, 2003, which claims priority fromAustralian Patent Application No. PS 1044, filed on Mar. 12, 2002.

This application claims the benefit of a 371 of PCT/AU03/00296 filed 12Mar. 2003.

FIELD OF THE INVENTION

The present invention relates broadly to a method of characterising amulti-layered structure during formation of said multi-layeredstructure, to a method of forming a multi-layered structure having aspecified coupling coefficient profile, and to an apparatus for forminga multi-layered structure having a specified coupling coefficientprofile.

BACKGROUND OF THE INVENTION

Typically, forming one-dimensional multi-layered structures in aphotosensitive material, e.g. so called writing of Bragg gratings,involves an interferometer in which two coherent light beams (typicallyin the UV wavelength range) are being directed along separate opticalpaths and brought to interference substantially within thephotosensitive material. Within the photosensitive material, refractiveindex changes are induced through the interaction between the lightbeams and the photosensitive material, and refractive index profiles areformed due to interference patterns, whereby grating structures arewritten.

The characterisation of gratings during the formation process has becomea significant aspect within the photonics technology field. For example,in one implementation of writing of long grating structures into anoptical fibre, the quality of the written grating depends on theaccuracy of matching of the velocity of an interference pattern change(sometimes referred to as travelling interference pattern) generated inthe grating writing setup to the velocity of the optical fibre beingtranslated through the interference region. In one such grating writingsetup, the control of the interference pattern velocity is achieved bymodulating the optical phase difference between the interfering beamse.g. by using optical modulators. Electronic control of the opticalphase difference and single frequency operation of the UV laser resultin an extreme accuracy, typically of the order of 10⁻¹⁰ that can beachieved by setting the velocity of the interference pattern using stateof the art electronic equipment and stabilising the UV laser.

Unfortunately, the accuracy of the fibre motion depends on the operationof mechanically inertial translation stages and is typically notexceeding 10⁻³–10⁻⁵ for the translation velocity. Therefore, accuratepassive synchronisation required may not be achievable with thetranslation stages currently available on the market.

Thus, an active feedback approach has been suggested to compensate forthe inaccuracies in the fibre motion control to achieve high fidelity ofsuch grating fabrication methods. Measuring characteristic parameters ofa grating under fabrication, comparing the measured parameters tospecified desired parameters, generating corrections to the gratingdesign parameters and closing a feedback loop by applying thecorrections to a grating writing control system in the process ofgrating writing is the underlying concept of relevant prior art. Gratingdesign serves as a reference in this approach, with the correctionsaccounting for random or systematic imperfections in the gratingfabrication process such as the above mentioned translation velocityinaccuracies. Therefore, the grating quality will ultimately depend onthe quality of the grating measurements and the quality of the feedbackloop rather than on the quality of the motion control.

A fibre Bragg grating can be fully described or characterised by eitherits coupling coefficient, or its impulse response, or its reflectioncoefficient. Those are sometimes referred to as grating design, temporalresponse and spectral response respectively and are related throughvarious transforms, e.g. impulse response is Fourier transform of thecomplex reflection coefficient, and the coupling coefficient can bededuced from the impulse response using inverse scattering methods.Experimentally, both amplitudes and phases of the coupling andreflection coefficients as well as the ones of the impulse response aretypically measured. Mathematically, the characteristic parameters withboth amplitude and phase can be expressed as complex functions and, toemphasize that, we will refer to the measurands throughout the presentdescription as to complex coupling and reflection coefficients, compleximpulse response function correspondingly.

Known techniques for fibre Bragg grating characterisation can becategorised in terms of the prime measurands mentioned above or in termsof the principle of operation. Naturally, both are often related. Theside diffraction techniques enable the direct measurements of thegrating coupling coefficient and are based on the external Braggdiffraction at the in-fibre Bragg grating. Optical low-coherencereflectometry (OLCR) methods have been shown to produce the impulseresponse of the grating device under investigation. The opticalfrequency domain characterisation (OFDC) methods are related to coherentinterferometry and provide spectral data for further analysis. Themethods of so called optical space domain reflectometry (OSDR) introducea small phase perturbation in the grating structure and the spatialvariation of its parameters is derived from the grating response to theperturbation. An “industry standard” modulation phase-shift (MPS)technique is based on measuring relative phase delay between the carrierand modulation sidebands in the spectrum of the intensity modulatedtunable laser and as such provides characterisation data in the spectraldomain.

Overall, a general disadvantage of most of the above mentioned prior arttechniques is an excessive amount of information being acquired whichmakes them relatively slow. This is because the measurements need to beconducted across a relevant wavelength range, and thus involvemeasurements of spectra and the associated necessary amount of data, andtuning of the laser source. Therefore, the grating fabrication speed mayneed to be slowed down to account for e.g. a slow scanning speed of afrequency-swept laser used in the OFDC approach. However, it has beenrecognised by the applicant that the excessive data collection may notbe needed at all, should a different approach to acquiringcharacterisation data be taken.

The present invention seeks to provide an alternative gratingcharacterisation method which can provide the basis for real-timegrating characterisation suitable for writing of gratings with theactive feedback approach.

SUMMARY OF THE INVENTION

In accordance with a first aspect of the present invention, there isprovided a method of characterising a multi-layered structure duringformation of said multi-layered structure, the method comprising thestep of extracting the complex coupling coefficient of the multi-layeredstructure being formed continuously or at intervals during themulti-layered structure formation process.

The step of extracting the complex coupling coefficient preferablycomprises measuring the complex reflectivity of the multi-layeredstructure at a wavelength outside of the bandgap of the multi-layeredstructure and calculating the complex coupling coefficient from themeasured complex reflectivity.

The step of calculating the complex coupling coefficient advantageouslyaccounts for the linear proportionality between the complex couplingcoefficient and the complex reflection coefficient at a wavelengthoutside the bandgap of the multi-layered structure.

In one embodiment, the complex reflectivity is measured for at least twowavelengths outside of the bandgap of the multi-layered structurecontinuously or at each interval.

The step of measuring the complex reflectivity of the multi-layeredstructure may comprise utilising a Sagnac/Michelson interferometersetup, wherein the multi-layered structure is located in the Sagnacloop.

The Sagnac/Michelson interferometer setup may comprise a 2×2 coupler.

The Sagnac/Michelson interferometer setup may comprise a 3×3 coupler.

In one embodiment, the method further comprises the step of controllinga phase rate offset in the phase measurement of the complex reflectivityof the multi-layered structure.

In a preferred embodiment, the method further comprises the step ofutilising a comparison of the extracted complex coupling coefficientsand a specified complex coupling coefficient profile of themulti-layered structure as a feedback during the formation process.

The multi-layered structure may comprise a Bragg grating. The gratingmay be formed in an optical waveguide. The waveguide may comprise anoptical fibre.

In accordance with a second aspect of the present invention, there isprovided an apparatus for forming a multi-layered structure of specifiedcomplex coupling coefficient profile, the apparatus comprising:

-   -   means for extracting the complex coupling coefficient of the        multi-layered structure being formed continuously or at        intervals during the multi-layered structure formation process,        and    -   a processing unit arranged, in use, to generate a feedback        signal for the formation process based on a comparison of the        extracted complex coupling coefficients and the specified        complex coupling coefficient profile.

The means for extracting the complex coupling coefficient preferablycomprises a measurement unit for measuring the complex reflectivity ofthe multi-layered structure at a wavelength outside of the bandgap ofthe multi-layered structure, and a unit for calculating the complexcoupling coefficient from the measured complex reflectivity.

The measurement unit is advantageously arranged, in use, to measure thereflectivity for at least two wavelengths outside of the bandgap of themulti-layered structure continuously or at each interval.

The unit for calculating the complex coupling coefficient preferablyaccounts for the linear proportionality between the complex couplingcoefficient and the complex reflection coefficient at a wavelengthoutside the bandgap of the multi-layered structure.

The measurement unit may comprise a Sagnac/Michelson interferometer,wherein the multi-layered structure is located in the Sagnac loop.

The Sagnac/Michelson interferometer may comprise a 2×2 coupler.

The Sagnac/Michelson interferometer may comprise a 3×3 coupler.

In one embodiment, the Sagnac/Michelson interferometer comprises a meansfor controlling a phase rate offset in the phase measurement of thecomplex reflectivity of the multi-layered structure.

The means for controlling the phase rate offset may comprise an opticalmodulator located in the Sagnac/Michelson loop on at least one side ofthe multi-layered structure. The modulator may comprise an acousto-opticmodulator or an electro-optic modulator.

The apparatus may further comprise a feedback unit for providing thegenerated feedback signal to a writing unit for forming themulti-layered structure. In one embodiment, the apparatus furthercomprises the writing unit.

In accordance with a third aspect of the present invention, there isprovided an active feedback fabrication method for forming amulti-layered structure, the method comprising the steps of extractingthe complex coupling coefficient of the multi-layered structure beingformed continuously or at intervals during the formation process, andutilising a comparison of the extracted complex coupling coefficientsand a specified complex coupling coefficient profile of themulti-layered structure as a feedback during the formation process.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the present invention will now be described, byway of example only, with reference to the accompanying drawings.

FIG. 1 is a schematic diagram illustrating a grating writing systemembodying the present invention.

FIG. 2 is a schematic diagram illustrating a grating portion in acharacterisation system embodying the present invention with incident,reflected and transmitted lightwaves shown.

FIG. 3 shows simulation example plots for a dispersionless square shapedDWDM filter embodying the present invention.

FIG. 4 shows simulation example plots for a chirped grating embodyingthe present invention.

FIG. 5 shows a Mach-Zehnder interferometric arrangement for acharacterisation system embodying the present invention.

FIG. 6 shows a Sagnac/Michelson interferometric arrangement for acharacterisation system embodying the present invention.

FIG. 7 shows a Sagnac/Michelson interferometric arrangement withfrequency shifters for a characterisation system embodying the presentinvention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The preferred embodiments described provide a grating characterisationsystem and method suitable for real-time characterisation for writing ofgratings in a waveguide using the active feedback approach.

In FIG. 1, a grating writing system 10 embodying the present inventionis shown. The system 10 comprises a UV laser source 12 providing a laserbeam 14 for the writing of the optical grating into an optical fibre 16mounted on a linear translation stage 18.

A suitable interferometer setup 24 is utilised to split the incominglaser beam 14 into two coherent writing beams 20, 22, and to bring thewriting beams 20, 22 to interference in an interference region 26located at the optical fibre 16 for writing the optical grating. Asshown in the inlet in FIG. 1, an interference pattern 28 is thus createdin the interference region 26 which extends along a finite length of thepropagating optical fibre 16 at any given point in time.

The interferometer setup 24 is arranged in a manner such that a relativephase difference is introduced between the writing beams 20, 22, whichresults in the interference pattern 28 to change continuously, i.e. theinterference fringes e.g. 30 move “across” the interference region 26with a velocity v_(P) as indicated by arrow 32. For the writing of along optical grating having a constant pitch, the velocity v_(P) ismatched to the translation velocity v_(F) of the optical fibre 16through the interference region 26, that is the velocity of thetranslation stage 18 as indicated by arrow 34. It will be appreciated bythe person skilled in the art that control of the relative phase shiftbetween the writing beams 20, 22 can also be used to write opticalgratings of varying pitch, such as chirped gratings.

The system 10 further comprises a feedback circuit 36 which is connectedto the optical fibre portion 16 mounted on the translation stage 18.

The feedback circuit 36 comprises an interrogation unit 40. In operationduring writing of an optical grating, a feedback signal is created as aresult of a measured interrogation output at the interrogation unit 40,and the feedback signal is communicated back to the interferometer setup24 via a feedback loop 50 for an active feedback approach to writing ofthe optical grating.

Turning now to FIG. 2, the underlying concept of the novel method ofcharacterisation of the optical grating during the writing process willnow be described. FIG. 2 shows a snapshot of a grating writing process.A grating portion 60 has been being written in an optical fibre 62 froma starting position z₁ to the position reached at the time of thesnapshot, z₂. The optical properties of the grating portion 60 can bedescribed by the following coupled mode equations:du(z,δ)/dz=+iδu(z,δ)+q(z)v(z,δ),  (1a)dv(z,δ)/dz=−iδv(z,δ)+q*(z)u(z,δ),  (1b)where q(z) and q*(z) are the complex coupling coefficient of the gratingportion 60 and its complex conjugate correspondingly, u(z,δ) is aforward propagating wave and v(z,δ) is a backward propagating wave, z isthe coordinate along the fibre 62 and

$\begin{matrix}{{\delta = {{\beta - \beta_{0}} \equiv {{\frac{2\pi}{\lambda}n} - \frac{\pi}{\Lambda_{0}}}}},} & (2)\end{matrix}$is the frequency detuning from the bandgap of the desired grating, withλ being the signal wavelength, n being the effective refractive index ofthe lightwave mode at the signal wavelength and Λ₀ being the gratingspatial period. Equations (1a), (1b) can be reduced to Ricatti equation

$\begin{matrix}{{{q^{*}(z)} = {{2i\;\delta\;{r\left( {z,\delta} \right)}} + \frac{\mathbb{d}{r\left( {z,\delta} \right)}}{\mathbb{d}z} + {{q(z)}{r^{2}\left( {z,\delta} \right)}}}},} & (3)\end{matrix}$for the local reflectivity r(z,δ)=v(z,δ)/u(z,δ) which is furthersimplified toq*(z)=2iδr(z,δ)  (4)assuming that the detuning δ from the Bragg wavelength (bandgap) islarge and the second and the third terms in the right hand side ofEquation (3) can be neglected. Equation (4) shows that the gratingcoupling coefficient is directly derived from a largely detuned spectralcomponent of the reflection spectrum. This spectral component evolves asthe grating is being written corresponding precisely to the gratingcoupling coefficient of the grating portion 60. It is important torealise that the measurements at a detuned wavelength have the advantageof low probe attenuation and, therefore, unlimited penetration of theprobe to all the “layers” of the grating. When the measurements areperformed using conventional characterisation methods, the probepropagation in the bandgap could be very small for strong gratingsresulting in distorted or incomplete data. By integrating Equations(1a), (1b) or by using (4), the complex coupling coefficient of thegrating portion 60 located, e.g. at z₂, can be expressed as a functionof the complex reflection coefficient at either end of the grating, i.e.at z₁ or z₂q*(z ₂)=−2iδr(z ₁,δ)exp[−2iδ(z ₂ −z _(1 )],)  (5a)q(z ₂)=−2iδr(z ₂,δ),  (5b)where we used the solutions for u(z,δ) and v(z,δ) in the large detuningapproximationu(z,δ)=u(z ₁,δ)exp[iδ(z−z ₁)],  (6a)v(z,δ)=v(z ₂,δ)exp[−iδ(z−z ₂)],  (6b)when the probe signal is incident from either the z₁ side or the z₂ sideof the grating correspondingly. In the latter case, the reflectioncoefficient is also redefined to r(z,δ)=u(z,δ)/v(z,δ) to obtain Equation(5b).

The obtained formulae (5) substantiate the concept of calculating thecomplex coupling coefficient of the grating portion under fabricationusing measured complex reflection coefficients.

A simulation example for a Dense Wavelength Division Multiplexer (DWDM)filter is shown in FIG. 3. The top two plots 70, 72 represent thereflection and the group delay of the square shaped filter with zerodispersion in the bandgap respectively. The amplitude and the phase ofthe grating coupling coefficient are shown in the middle plots 74, 76and they have been derived from the reflection and the group delayspectra using an inverse scattering technique. The difference betweenthis exact value of the grating coupling coefficient q*(z) and the valueobtained using derived approximate Equation (4) represents the higherorder terms in Equation (3) and is shown in the bottom plots 78, 80. Ascan be seen from the plots 78, 80, the amplitude error in the simulationexample is about 2·10⁻³.

Another simulation example for a chirped grating dispersion compensatoris shown in FIG. 4, plots 81, 82, 84, 86, 88 and 90. A comparison of theresults for this grating with the results for the previous one indicatesthat the accuracy of the method is somewhat design sensitive whichshould certainly be expected given the higher order terms in Equation(3).

The examples above demonstrate numerically the correctness of theanalytically derived relationship (4) between the complex couplingcoefficient of a local portion of the grating under fabrication and thecomplex reflection coefficient. The simplicity of the relationshiprepresents a significant advantage for creating a feedback signal duringthe writing of a grating in an active feedback writing technique.

Since we have revealed the relationships between the complex couplingcoefficients of the multi-layered structure under fabrication and themeasured complex reflection coefficients, a preferred embodiment formeasuring the complex reflection coefficients will now be described.

Measurements of the complex reflection coefficient can be performed in anumber of different ways e.g. using measurement setups similar to OFDCor MPS referred to above, however, without the need to sweep thewavelength of the coherent laser source.

One such example measurement setup 100 is shown in FIG. 5. The setup 100comprises a laser source 110 and an optical circuit comprising of aMach-Zehnder interferometer 112. One arm of the Mach-Zehnder 112comprising a circulator 114 for directing the light signal into anoptical fibre 116 into which a grating 118 is being progressivelywritten, and for returning a reflected light signal from the grating 118back into that arm. In the example embodiment, 3 dB couplers 120, 122are utilised to form the Mach-Zehnder interferometer configuration.

A processing unit 124 comprises a detector unit 126 for detecting lighttransmitted through the optical fibre 116, and a detection unit 128 fordetecting the output of the Mach-Zehnder interferometer 112. It will beappreciated by a person skilled in the art that thus the setup 100 canbe utilised to measure the complex coupling coefficients of the localportion of the grating 118 under fabrication, since both amplitude andphase information are available at the processing unit 124, which inturn can be utilised to create a feedback signal 130 to the gratingwriting apparatus (not shown) during the writing of the grating 118 inan active feedback writing technique.

It is emphasised that in the setup 100, the wavelength of the lasersource 110 does not need to be scanned or tuned to obtain spectral dataas in the prior art. Rather, a fixed wavelength detuned from the bandgapof the desired optical grating 118 is used, as in accordance with thepresent invention, no spectral data is required, but rather a continuedmeasurement of the complex reflection coefficient of the grating portionunder fabrication only.

While the setup 100 represents an example embodiment of the presentinvention, it will be appreciated by the person skilled in the art thatthis setup may be susceptible to environmental fluctuations of theMach-Zehnder interferometer 112. Furthermore, since the exact centrewavelength of the ultimate grating 118 and thus the detuning δ inequations 6(a) and 6(b) may not be known exactly, the measurements arepreferably conducted at two separate fixed wavelengths outside of thebandgap of the grating 118 to eliminate the actual centre wavelengthfrom the calculations. However, it will be appreciated that neverthelessthe embodiment shown in FIG. 5 still achieves the advantage of reducingthe amount of data required for creating a feedback signal in an activefeedback grating writing technique.

Another preferred embodiment incorporating a novel approach forconducting the measurement of the complex reflection coefficient willnext be described with reference to FIG. 6.

The approach described in relation to this embodiment is based on thefundamental relationship

$\begin{matrix}{\frac{r\left( {z_{1},\delta} \right)}{r^{*}\left( {z_{2},\delta} \right)} = {- \frac{t(\delta)}{t^{*}(\delta)}}} & (7)\end{matrix}$which exists between the reflection coefficients for both directions ofthe probe signal incidence and the transmission coefficient which isindependent of that direction. The existence of such a relationshipsuggests an interferometric characterisation technique with thereflected and transmitted signals interfering with each other. This canbe achieved by placing the grating under fabrication 202 in a Sagnacloop 204 which, by virtue of the grating 202 in the loop 204, becomes acombined Sagnac/Michelson interferometric arrangement 200 as shown inFIG. 6. The output signals of the arrangement 200 in the case of 50/50coupler 206 are as follows

$\begin{matrix}{{\frac{I_{left}}{I_{0}} = {T + {R\;\cos^{2}\Phi}}},} & \left( {8a} \right) \\{{\frac{I_{right}}{I_{0}} = {R\;\sin^{2}\Phi}},} & \left( {8b} \right)\end{matrix}$where I₀ is the interferometer input at 208 and I_(left), and I_(right)are the interferometer output signal intensities at 210 and 212respectively, T=|t|² and R=|r|² are the grating transmission andreflection correspondingly, and the phase Φ is determined by both thegrating phase and the imbalance of the Michelson interferometer arms L₁and L₂ due to both generally asymmetric location of the grating 202 inthe Sagnac loop 204 and the dynamically changing grating length L₂Φ=β(L ₁ +L ₂ −L ₃)−(β₀ L ₂ +arg r)≡Ξ−Θ.  (9)

The output signals can be processed, e.g. by adding and subtractingthem, either optically or electronically after their detection by e.g.balanced pair of detectors (not shown),

$\begin{matrix}{{\frac{I_{left} + I_{right}}{I_{0}} = {T + R}},} & \left( {10a} \right) \\{\frac{I_{left} - I_{right}}{I_{0}} = {T + {R\;\cos\; 2{\Phi.}}}} & \left( {10b} \right)\end{matrix}$

As Φ is being dynamically changed during the grating fabrication processat a certain rate defined primarily by the fibre translation velocityand the grating design, the AC terms (Φ-dependent) can be separated fromthe DC terms by e.g. using Fourier transform methods.

If the coupler 206 in the arrangement 200 shown in FIG. 6 slightlydeviates from the 50/50 splitting ratio case, i.e. K=½(1−δK), then

$\begin{matrix}{\frac{I_{left} - I_{right}}{I_{0}} = {T + {R\;\cos\; 2\Phi} - {4\delta\; K\sqrt{TR}\sin\;{\Phi.}}}} & (11)\end{matrix}$Therefore, using e.g. Fourier transform methods the effect of thecoupling ratio variations on the Φ calculation accuracy can beminimised. Also, the coupling ratio can be intentionally modulated andlocked to the 50/50 value by applying e.g. lock-in techniques.

Returning now to Equation (9), it will be appreciated that uncertaintiesare attached to both β and (L₁+L₂−L₃) due to environmental fluctuations.However, if in the experiment the data are collected at two wavelengths,then the phase term Θ determined by only the fibre translation rate andthe actual current grating phase can be calculated:

$\begin{matrix}{\Theta = {{{\beta_{0}L_{2}} + {\arg\; r}} = {{- \Phi} + {\beta{\frac{\Delta\Phi}{\Delta\beta}.}}}}} & (12)\end{matrix}$Thus, the effect of likely significant environmental fluctuations of theMichelson interferometer arms (changes in L₁ and L₃) can be dramaticallyreduced by using at least two fixed single-frequency stabilized lasersto perform the measurements at two wavelengths at least. Importantly,the measurement noise can be significantly reduced by optical filteringof only the narrow linewidth signals associated with thefixed-wavelength laser sources (not shown).

Referring now to FIG. 7, another preferred embodiment of implementingthe present invention during the writing of a grating 302 will bedescribed.

The signals I_(left) at 310 and I_(right) at 312 resulting from theoutputs of the interferometric arrangement 300 shown in FIG. 7 can bedescribed by the following expressions

$\begin{matrix}\begin{matrix}{\frac{I_{left} + I_{right}}{I_{0}} = {{T\;\alpha_{1}^{2}\alpha_{2}^{2}} + {R\left( {{\alpha_{1}^{4}\cos^{2}\kappa\; L_{0}} + {\alpha_{2}^{4}\sin^{2}\kappa\; L_{0}}} \right)} -}} \\{\sqrt{TR}\alpha_{1}{\alpha_{2}\left( {\alpha_{1}^{2} - \alpha_{2}^{2}} \right)}\sin\; 2\;\kappa\; L_{0}\sin\;\Phi}\end{matrix} & \left( {13a} \right) \\\begin{matrix}{\frac{I_{left} - I_{right}}{I_{0}} = {{{- T}\;\alpha_{1}^{2}\alpha_{2}^{2}\cos\; 4\kappa\; L_{0}} +}} \\{{{R\left( {{\alpha_{1}^{4}\cos^{2}\kappa\; L_{0}} - {\alpha_{2}^{4}\sin^{2}\kappa\; L_{0}}} \right)}\cos\; 2\;\kappa\; L_{0}} -} \\{\sqrt{TR}\alpha_{1}{\alpha_{2}\left\lbrack {{\left( {{3\alpha_{1}^{2}} + \alpha_{2}^{2}} \right)\cos^{2}\kappa\; L_{0}} -} \right.}} \\{{\left. {\left( {{3\alpha_{2}^{2}} + \alpha_{1}^{2}} \right)\sin^{2}\kappa\; L_{0}} \right\rbrack\sin\; 2\kappa\; L_{0}\sin\;\Phi} +} \\{{R\alpha}_{1}^{2}\alpha_{2}^{2}\sin^{2}2\kappa\; L_{0}\cos\; 2\Phi}\end{matrix} & \left( {13b} \right)\end{matrix}$where I₀ is the input signal at 308, K=sin²κL₀ is the coupling ratio ofthe coupler, with κ and L₀ being the coupling coefficient and the lengthof the coupling region, α₁ and α₂ are the one-way transmissioncoefficients in the corresponding Michelson arms which are defined byboth the splice losses of the grating to the arrangement and thediffraction efficiencies of the frequency shifters.

Using the frequency shifters 301, 303 shown in FIG. 7 has been motivatedby the following potential advantages:

-   -   (a) Ability to normalize the reflection responses from the        opposite ends of the grating which may otherwise be different        due to e.g. different splice losses at the ends of the grating.        Minimizing the corresponding oscillating term ∝(α₁ ²−α₂ ²)sin Φ        (see Equation (13a)) can be achieved by appropriate control of        the diffraction efficiency of the frequency shifters.    -   (b) Ability to control the rate of the phase change Θ by        changing the shifting frequencies Ω₁ and Ω₂:        Θ=β₀ ∫v _(f)(ti dt+arg r+∫[Ω₁(t)−Ω₂(t)]dt  (14)        which gives a lot of flexibility in detecting and separating,        through control of the offset introduced, the terms proportional        to Θ and 2Θ or Φ and 2Φ in Equations (13). The frequency shift        could be continuously (synchronously) changed so that e.g. the        corresponding accumulated phase change would represent the        control signal for the grating writing system. Thus, a pure        phase error signal acquired due to either imperfect translation,        or imperfect fibre diameter, or due to any other reason, could        be obtained without the need for further processing (assuming        that the dual-wavelength processing has been completed). This        signal would be used to lock-in to the theoretical grating        phase. The rate of the “linearised” (control signal subtracted)        phase change can be adjusted to a convenient or an optimum        frequency defined by the lock-in used, phase noise statistics,        etc. It can e.g. be chosen such that the interferometric        arrangement operates at a dark fringe with respect to the ‘dark’        (right) output of the interferometer to reduce the effect of the        laser source noise on the signal at that output.

It will be appreciated by the person skilled in the art that numerousmodifications and/or variations may be made to the present invention asshown in the specific embodiments without departing from the spirit orscope of the invention as broadly described. The present embodimentsare, therefore, to be considered in all respects to be illustrative andnot restrictive.

For example, multi-layered structures can be fabricated using variousknown techniques of forming such structures, including one or more ofthe group of photo-induced refractive index variation in photosensitivewaveguide materials, etching techniques including etching techniquesutilising a phasemask, and epitaxial techniques. Furthermore, while thepreferred embodiments have been described in the context of1-dimensional Bragg gratings, the present invention does extend tomulti-dimensional multi-layered structures. Such structures haveapplications e.g. as photonic bandgap structures.

In the claims that follow and in the summary of the invention, exceptwhere the context requires otherwise due to express language ornecessary implication the word “comprising” is used in the sense of“including”, i.e. the features specified may be associated with furtherfeatures in various embodiments of the invention.

1. A method of characterising a multi-layered structure during formationof said multi-layered structure, the method comprising extracting,continuously or at intervals during the formation process, a complexcoupling coefficient of the multi-layered structure being formed.
 2. Amethod as claimed in claim 1, wherein extracting the complex couplingcoefficient comprises measuring a complex reflectivity of themulti-layered structure at a wavelength outside of a bandgap of themulti-layered structure and calculating the complex coupling coefficientfrom the measured complex reflectivity.
 3. A method as claimed in claim2, wherein calculating the complex coupling coefficient uses a linearproportionality between the complex coupling coefficient and themeasured complex reflectivity.
 4. A method as claimed in claim 2,wherein the complex reflectivity is measured, continuously or at eachinterval, for at least two wavelengths outside of the bandgap of themulti-layered structure.
 5. A method as claimed in claim 2, whereinmeasuring the complex reflectivity of the multi-layered structurecomprises utilising a Sagnac/Michelson interferometer setup, wherein themulti-layered structure is located in the Sagnac loop.
 6. A method asclaimed in claim 5, wherein the Sagnac/Michelson interferometer setupcomprises a 2×2 coupler.
 7. A method as claimed in claim 5, wherein theSagnac/Michelson interferometer setup comprises a 3×3 coupler.
 8. Amethod as claimed in claim 5, wherein the method further comprisescontrolling a phase rate offset in the phase measurement of the complexreflectivity of the multi-layered structure.
 9. A method as claimed inclaim 1, wherein the method further comprises utilising a comparison ofthe extracted complex coupling coefficient and a specified complexcoupling coefficient profile of the multi-layered structure as afeedback during the formation process.
 10. A method as claimed in claim1, wherein the multi-layered structure comprises a Bragg grating.
 11. Amethod as claimed in claim 10, wherein the grating is formed in anoptical waveguide.
 12. A method as claimed in claim 11, wherein thewaveguide comprises an optical fibre.
 13. An apparatus for forming amulti-layered structure of specified complex coupling coefficientprofile, the apparatus comprising: a complex coupling coefficientextractor for extracting a complex coupling coefficient of themulti-layered structure being formed, wherein the complex couplingcoefficient is extracted continuously or at intervals during themulti-layered structure formation process, and a processing unitarranged, in use, to generate a feedback signal for use in the formationprocess based on a comparison of the extracted complex couplingcoefficient and the specified complex coupling coefficient profile. 14.An apparatus as claimed in claim 13, wherein the complex couplingcoefficient extractor comprises a measurement unit for measuring acomplex reflectivity of the multi-layered structure at a wavelengthoutside of a bandgap of the multi-layered structure, and a calculatingunit for calculating the complex coupling coefficient from the measuredcomplex reflectivity.
 15. An apparatus as claimed in claim 14, whereinthe calculating unit for calculating the complex coupling coefficientuses a linear proportionality between the complex coupling coefficientand the measured complex reflectivity.
 16. An apparatus as claimed inclaim 14, wherein the measurement unit is arranged, in use, to measure,continuously or at each interval, the reflectivity for at least twowavelengths outside of the bandgap of the multi-layered structure. 17.An apparatus as claimed in claim 14, wherein the measurement unitcomprises a Sagnac/Michelson interferometer, wherein the multi-layeredstructure is located in the Sagnac loop.
 18. An apparatus as claimed inclaim 17, wherein the Sagnac/Michelson interferometer comprises a 2×2coupler.
 19. An apparatus as claimed in claim 17, wherein theSagnac/Michelson interferometer comprises a 3×3 coupler.
 20. Anapparatus as claimed in claim 17, wherein the Sagnac/Michelsoninterferometer comprises a means for controlling a phase rate offset inthe phase measurement of the complex reflectivity of the multi-layeredstructure.
 21. An apparatus as claimed in claim 20, wherein the meansfor controlling the phase rate offset comprises an optical modulatorlocated in the Sagnac/Michelson loop on at least one side of themulti-layered structure.
 22. An apparatus as claimed in claim 21,wherein the modulator comprises an acousto-optic modulator or anelectro-optic modulator.
 23. An apparatus as claimed in claim 13,wherein the apparatus further comprises a feedback unit for providingthe generated feedback signal to a writing unit for forming themulti-layered structure.
 24. An apparatus as claimed in claim 23,wherein the apparatus further comprises the writing unit.
 25. An activefeedback fabrication method for forming a multi-layered structure, themethod comprising: extracting, continuously or at intervals during theformation process, a complex coupling coefficient of the multi-layeredstructure being formed, and utilising a comparison of the extractedcomplex coupling coefficient and a specified complex couplingcoefficient profile of the multi-layered structure as a feedback duringthe formation process.